Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

question6.mw
How you can see, in the following exercise I built five plots, every one with the graph of two functions. The exersise say that I must find coordinates of any intersection. I think I can do it with solve command. However, I want point out coordinates of  intersections inside the plots. Probably exists a command or a parameter to success with my objetive. How can I do it?

NULL

*** e2.103

 

Plot the following couples of formulae; note in particular the contrasting forms of two curves in each case, and find the coordinates of any intersections.

i)    {x, x^3},

ii)    {x^2, x^4},

iii)    {1/x, 1/x^2},

 iv)   {x^2, sqrt(x)},

 v)   {x^3, abs(x^(1/3))}

 

restart:

NULL

Thank you for helping me;
Greetings;
Lic. Marcus Vinicio Mora Salas;
Chemist;
Postgraduate student at University of Costa Rica;

Download question6.mw

restart:

``

K__vxa[1] := 2.0154553049*10^17

0.2015455305e18

(1)

`#mrow(mi("\`K__vxa\`"),mfenced(mn("1"),open = "[",close = "]"))`+K__vxa[1]

`#mrow(msub(mi("\`K"),mi("vxa\`")),mfenced(mn("1"),open = "[",close = "]"))`+0.2015455305e18

(2)

``

Download Prj.mw

 

The Bohemian Matrix Calendar 2022 is up!  You may find it at https://rcorless.github.io/ (four versions: letter/A4 paper, Sunday/Monday start to the week).

It prints quite well (with proper equipment).  I wish you all the best for 2022.

 

(Maple 2015)

Why is m1(t) not evaluated correctly when I use a compound condition?

restart:
m2(t) = piecewise(x1(t) < c and v1(t) < 0, 1,  0);
       m2(t) = piecewise(x1(t) < e2 and v1(t) < 0, 1, 0)

m1(t) = piecewise(x1(t) = c and v1(t) > 0, 0,  1);
                           m1(t) = 1

This doesn't happen for simple conditions
 

m2(t) = piecewise(x1(t) < c, 1,  0);
m1(t) = piecewise(x1(t) = c, 0,  1);
               m2(t) = piecewise(x1(t) < c, 1, 0)
               m1(t) = piecewise(x1(t) = c, 0, 1)

TIA

In Matlab I can copy a Figure as a vector graphic and paste it into Adobe Illustrator, where it is perfectly scalable and it can be exported as a say 100cm by 100cm 300 DPI jpg file.

In Maple I struggle to produce similar quality files

Thanks,

Peter

question5.mw

In document uploaded I tried to write a code to get as output 11 plots. I would like a format as this: 9 plots in 3 columns an 3 rows, and a fourth row with two center plots. To explain me better, I drew a rustic sketch of what I want, basically something like this:

However I tried but I fail and my output is horrible. So, I want to ask: Does exists some option to the plot[display] command or should I try another aproach?

Thank you for helping me;
Greetings;
Lic. Marcus Vinicio Mora Salas;
Chemist;
Postgraduate student.

As part of my course work I've encountered a block wherein I need to convert a 4th order TF to a SmithForm but am unable to do so.

Can anyone help me with the code as attatched.

A := Matrix([[(.3384*x^3-26.13*x^2-.3659*x+0.1678e-1)/(s^4+3.068*s^3-3.362*s^2-.5748*s+.7598), (.4755*s^3-25.3*s^2-51.36*s-1.387)/(s^4+3.068*s^3-3.362*s^2-.5748*s+.7598)], [(-.3349*s^3+18.21*s^2+.3487*s-0.5939e-1)/(s^4+3.068*s^3-3.362*s^2-.5748*s+.7598), (-.3107*s^3+17.81*s^2+35.49*s+1.027)/(s^4+3.068*s^3-3.362*s^2-.5748*s+.7598)]])

Matrix(%id = 36893488152131246308)

(1)

"->"

Error, (in gcdex) invalid arguments

 

"->"

SmithForm(Matrix(%id = 36893488152131266788))``

(2)

with(LinearAlgebra)

NULL

S := SmithForm(A, s)

Error, (in gcdex) invalid arguments

 

with(LinearAlgebra); A := Matrix([[1, 2*x, 2*x^2+2*x], [1, 6*x, 6*x^2+6*x], [1, 3, x]])

Matrix(%id = 36893488152361731844)

(3)

S := SmithForm(A, x)

Matrix(%id = 36893488152348668020)

(4)

NULL

Download SmithForm.mw

Hello!

how to find the solutions of a system of recursive equations? And the plot too.

I tried but...

B := rsolve({a(0) = 0, a(i) = (1 + 10^(-5)*(0.01*(i - 1) - 0.007)/0.0001)*a(i - 1) + 0.1*10^(-5)*c(i - 1), c(0) = 0, c(i) = 0.01*10^(-5)*(i - 1)/0.0001*a(i - 1) + (1 - 10^(-5))*0.1*c(i - 1)}, {a(i), c(i)}, 'genfunc'(t));
B := rsolve({a(i) = (0.9983000000 + 0.001000000000 i) a(i - 1)

   + 0.000001000000000 c(i - 1), 

  c(i) = 0.001000000000 (i - 1) a(i - 1) + 0.09999900000 c(i - 1)

  }, {a(i), c(i)}, genfunc(t))

rsolve_for_system_of_recursive_equations.mw

thanks

This is a simple problem of Chemistry. I solved the exercise, but there are three aspects I don't like about output:
1) Even kg*m2 *s-2 = J (SI unit to energy) and both are correct, one must be explicit with units in order to be totally clear, so I need an output with units of J/mol and not kg*m2 *s-2 mol-1.
2) I had to hardcode number of significant figures, so I had to analize quantitys in order to determine this number, wich as you can see, is three. I think Maple can compute significant figures automatically, but I could not find the command in documentation and even in this case is not totally needed, I would like to learn how do it because it could be very useful for more complex expressions.
3) Finally, output must be expressed using scientific notation, it's say enthalpy = 10.4*104 J/mol.
Therefore: How can I get adecuate output?
Thank you for helping me;
Greetings;
Lic. Marcus Vinicio Mora Sallas;
Chemist;
Postgraduate student. question4.mw

*** e1.501

 

Using this equation attributed to Clausius and Clapeyron,

ln(P[2]/P[1]) = Delta*H[vap]/R 1/T[1]-1/T[2]

and these data for the vapour pressure of liquid mercury at the indicated temperatures,

      P =  1.6 10^(-4) Pa at T = 273.15 K and P = 36.4 Pa at T = 373.15 K

estimate the enthalpy change Delta*H[vap] for vapourization of mercury over this range of temperature.

 

p := [1.6e-4*Unit('Pa'), 36.4*Unit('Pa')]:

Delta(H[vap]) = 0.105e6*Units:-Unit(m^2*kg/(s^2*mol*K))*Units:-Unit(K)

``

Download question4.mw

system_of_PDE.mw

NULL

NULL

Digits := 30; with(PDEtools); with(plots); Ops1 := numpoints = 100; Ops2 := color = magenta; Ops3 := color = blue; Ops4 := color = "BlueViolet"; Ops5 := axes = boxed, shading = zhue, orientation = [40, 50]; a := 0; b := 1; Tf := .5

axes = boxed, shading = zhue, orientation = [40, 50]

 

.5

(1)

E := 1480

1480

(2)

Ebes := 5990

5990

(3)

n0 := 900000

900000

(4)

ro := 1200

1200

(5)

m := 12.6

12.6

(6)

f := sig(x, t)-Ebes*`&varepsilon;ij`(x, t)

sig(x, t)-5990*`&varepsilon;ij`(x, t)

(7)

n := 900000*exp(-(sig(x, t)-E*`&varepsilon;ij`(x, t))/m)

900000*exp(-0.793650793650793650793650793651e-1*sig(x, t)+117.460317460317460317460317460*`&varepsilon;ij`(x, t))

(8)

NULL

P := 5

5

(9)

w := 4

4

(10)

k := 7

7

(11)

i := 5

5

(12)

eq1 := diff(sig(x, t), x, x) = ro*(diff(sig(x, t), x, x))/E+ro*(diff(sig(x, t), t)-Ebes*f/(9000000*exp(-(sig(x, t)-E*`&varepsilon;ij`(x, t))/m)))*(1+f/m)/(9000000*exp(-(sig(x, t)-E*`&varepsilon;ij`(x, t))/m))

diff(diff(sig(x, t), x), x) = (30/37)*(diff(diff(sig(x, t), x), x))+(1/7500)*(diff(sig(x, t), t)-(599/900000)*(sig(x, t)-5990*`&varepsilon;ij`(x, t))/exp(-0.793650793650793650793650793651e-1*sig(x, t)+117.460317460317460317460317460*`&varepsilon;ij`(x, t)))*(1+0.793650793650793650793650793651e-1*sig(x, t)-475.396825396825396825396825397*`&varepsilon;ij`(x, t))/exp(-0.793650793650793650793650793651e-1*sig(x, t)+117.460317460317460317460317460*`&varepsilon;ij`(x, t))

(13)

 

eq2 := diff(`&varepsilon;ij`(x, t), t) = f/(9000000*exp(-(sig(x, t)-E*`&varepsilon;ij`(x, t))/m))

diff(`&varepsilon;ij`(x, t), t) = (1/9000000)*(sig(x, t)-5990*`&varepsilon;ij`(x, t))/exp(-0.793650793650793650793650793651e-1*sig(x, t)+117.460317460317460317460317460*`&varepsilon;ij`(x, t))

(14)

NULL

sys := {eq1, eq2}

{diff(diff(sig(x, t), x), x) = (30/37)*(diff(diff(sig(x, t), x), x))+(1/7500)*(diff(sig(x, t), t)-(599/900000)*(sig(x, t)-5990*`&varepsilon;ij`(x, t))/exp(-0.793650793650793650793650793651e-1*sig(x, t)+117.460317460317460317460317460*`&varepsilon;ij`(x, t)))*(1+0.793650793650793650793650793651e-1*sig(x, t)-475.396825396825396825396825397*`&varepsilon;ij`(x, t))/exp(-0.793650793650793650793650793651e-1*sig(x, t)+117.460317460317460317460317460*`&varepsilon;ij`(x, t)), diff(`&varepsilon;ij`(x, t), t) = (1/9000000)*(sig(x, t)-5990*`&varepsilon;ij`(x, t))/exp(-0.793650793650793650793650793651e-1*sig(x, t)+117.460317460317460317460317460*`&varepsilon;ij`(x, t))}

(15)

NULL

IBC1 := {sig(0, t) = P*sin(w*k*i), sig(10, t) = P*sin(w*k*i), sig(x, 0) = 0, sig(x, 1) = 0, `&varepsilon;ij`(x, 0) = 0}

{sig(0, t) = 5*sin(140), sig(10, t) = 5*sin(140), sig(x, 0) = 0, sig(x, 1) = 0, `&varepsilon;ij`(x, 0) = 0}

(16)

S := 1/100; Ops := spacestep = S, timestep = S; Sol1 := pdsolve(sys, IBC1, [sig, `&varepsilon;ij`], numeric, time = t, range = a .. b, Ops)

1/100

 

spacestep = 1/100, timestep = 1/100

 

Error, (in pdsolve/numeric) unable to handle elliptic PDEs

 

``

Download system_of_PDE.mw

Sometimes its easier when doing math in maple input mode to use first the 2d maple input mode and convert this to maple input
Is there a hotkey assigned in Maple to do this toggling from 1d input to 2d input ( also from 1d output to 2d output  )

Now it must be done by mouse

In relation with the following code and its respective output:

I want get an output in wicht left side of equalitys be expressed in radical terms and not in terms of trigonometric expressions. I tried convert(expr, radical), but the result is not that I want. Could someone help me please? Also I want to know if exists a method to avoid hardcoding list of the forloop other than [seq(i, i = 1..5)];

Thank you for helping me;
Greetings;
Lic. Marcus Vinicio Mora Salas;
Chemist;
postgraduate student in University of Costa Rica

Do someone tell me how can I solve this exersise using a created procedure? Also I would like to know if using a procedure is useful and if in that form code lines will be reduce. If procedures are not useful. What is the best aproach?

Here the exercise and the code:

Before to begin to learn Maple, I used to do math with python. I usually built function and classes in order to reduce code lines and to generalize the problem, but I don't know if this aproach is useful with Maple. In fact, I have another question. Is it possible to write in a document some codeblocks using Maple and another using python? If answer is yes, how can I do it?

Thank you for helping me;
Greetings;
Lic. Marcus Vinicio Mora Salas
Chemist

Hi MaplePrimes team,

Is there a generalized way to fill an extremely CONCAVE closed 3d parametric plane curve in Maple with spacecurve command (NO implicitplot3d), preferably without doing any multi-decomposition or creating a particular skeleton, or algorithm/programming?

Here my example:

 

#Circle of reference
R0 := 1:
C0 := t-> < cos(t), sin(t), 0 >:

#Variable radius
R := t-> R0*(1 + 1/2*sin(t)):

#Variable phase
Dt := t-> Pi/2*sin(2*t):

#CONCAVE Curve
C := t-> R(t)*C0(t - Dt(t)):
'C(t)' = C(t);

#Range
t1, t2 := 0, 2*Pi:

#Plot
GC := spacecurve(C(t), t = t1..t2, color = "Red", thickness = 3
, linestyle = solid
, scaling = constrained, axes = frame, orientation = [50,40,0]):
GC;

We know how to do it easily for any convex 3d plane curve (circle, ellipse, regular polygon, etc ...).

We also know how to do it for 2d curve with the Maple’s plot option filled = true but obviously not in 3d.

Thank you for your time.

Best.

Guy.

Hello, I am new with Maple. I am using because I am taking a course in my college where I need it. I have the following problem: How it can be seen in image, code is not been adecuatelly executed, because I need numerical values at output. I think this problem is because a configuration issue, but I am not sure.

How can I restore default configuration in order to try a solution for this issue?

First 342 343 344 345 346 347 348 Last Page 344 of 2216